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In this paper, by invariant-based inverse engineering, we design classicaldriving fields to transfer quantum fluctuations between two suspended membranesin an optomechanical cavity system. The transfer can be quickly attainedthrough a non-adiabatic evolution path determined by a so-called dynamicalinvariant. Such an evolution path allows one to optimize the occupancies of theunstable "intermediate" states thus the influence of cavity decays can besuppressed. Numerical simulation demonstrates that a perfect fluctuationtransfer between two membranes can be rapidly achieved in one step, and thetransfer is robust to both the amplitude noises and cavity decays.

Invariant-based inverse engineering for fluctuation transfer between membranes in an optomechanical cavity system